The equation x^3 + 5x^2 +1 = 7 models the volume of a shipping container where x is the width. Graph the equation to find the width of the box.

Question

Please answer this question I have asked it 2 times before and no one answers.

Choose one of these answers it is Multiple Choice

 

a. 1 ft.

b. 2 ft.

c. 4 ft.

d. 7 ft.

Answer 1

We can check by plugging possible solution values into the equation and seeing which one works.

 

a) 1 ft:

(1)³ +5(1)² + 1

=1 + 5 + 1

=7

 

So 1 ft is a valid choice for the width.

 

Since x³ and x² are both increasing for x>0, the volume gets bigger as x increases.  This means that any value of x which is greater than 1 will give a volume greater than 7.  We don't need to check any of the other possibilities, since they are all greater than 1.